Limit behavior of solutions of ordinary linear differential equations.
Limit Circle Results for Second Order Equations.
Limit cycle for the Brusselator by He's variational method.
Limit cycles for a class of polynomial systems and applications.
Limit cycles for vector fields with homogeneous components
We study planar polynomial differential equations with homogeneous components. This kind of equations present a simple and well known dynamics when the degrees (n and m) of both components coincide. Here we consider the case and we show that the dynamics is more complicated. In fact, we prove that such systems can exhibit periodic orbits only when nm is odd. Furthermore, for nm odd we give examples of such differential equations with at least (n+m)/2 limit cycles.
Limit cycles in a Kolmogorov-type model.
Limit cycles in the equation of whirling pendulum with autonomous perturbation
The two-parameter Hamiltonian system with the autonomous perturbation is considered. Via the Mel’nikov method, existence and uniqueness of a limit cycle of the system in a certain region of a two-dimensional space of parameters is proved.
Limit cycles in the Holling-Tanner model.
This paper deals with the following question: does the asymptotic stability of the positive equilibrium of the Holling-Tanner model imply it is also globally stable? We will show that the answer to this question is negative. The main tool we use is the computation of Poincaré-Lyapunov constants in case a weak focus occurs. In this way we are able to construct an example with two limit cycles.
Limit cycles of a class of Hilbert's sixteenth problem presented by fractional differential equations.
Limit Cycles of Perturbations of a Class of Quadratic Hamiltonian Vector Fields
We prove that in quadratic perturbations of generic Hamiltonian vector fields with two saddle points and one center there can appear at most two limit cycles. This bound is exact.
Limit properties of solutions of singular second-order differential equations.
Limiting phase trajectories and resonance energy transfer in a system of two coupled oscillators.
Linear differential equations of the 2nd order whose principal solution has unbounded logarithmic derivative
Linear differential equations of the second order with elementary basic central dispersions
Linear differential equations with quasiperiodic coefficients
Linear differential Lappo-Danilevskii systems
Linear differential Lappo-Danilevskii systems
The class of linear differential systems with coefficient matrices which are commutative with their integrals is considered. The results on asymptotic equivalence of these systems and their distribution among linear systems are given.
Linear differential transformations of the 2nd order as a representation of an abstract model
Linear fractionally damped oscillator.
Linear ODEs and -modules, solving and decomposing equations using symmetry methods.